I am a British/French topos theorist working in Italy. My goal is to expose the richness of toposes theory through the special case of monoid actions, so as to make toposes accessible to the wider mathematical community.
Research Interests
Currently I am studying topological monoids through their toposes of (right) actions on sets, and the geometric morphisms between these. A long-term goal for this work is to identify and apply the natural extensions of known results and constructions for groups to arbitrary monoids.
Publications/Preprints
1) MR, Toposes of Topological Monoid Actions, preprint, submitted to Compositionality (2021) arxiv:2105.00772
2) MR, Supercompactly and Compactly Generated Toposes, preprint, submitted to TAC (2021) arxiv:2101.04015
3) J. Hemelaer, MR, Solution to a problem of FitzGerald, Semigroup Forum (2021)
https://link.springer.com/content/pdf/10.1007/s00233-021-10170-5.pdf
4) J. Hemelaer, MR, An essential, hyperconnected, local geometric morphism that is not locally connected, Applied Categorical Structures (2021)
https://link.springer.com/article/10.1007/s10485-020-09626-6
5) J. Hemelaer, MR, Monoid Properties as Invariants of Toposes of Monoid Actions, Applied Categorical Structures (2020)
https://link.springer.com/article/10.1007/s10485-020-09620-y
6) MR, Toposes of Discrete Monoid Actions, preprint (2019) arxiv:1905.10277
Conferences attended: Category Theory 2019 (Edinburgh), PSSL 105 (Palermo), TACL 2019 (Nice), 6th Workshop on Formal Topology (Birmingham), Toposes in Como 2018 (Como), SYCO6 (Leicester), Topics in Category Theory 2020 (Edinburgh), Category Theory 2021 (Genova).
Future Conferences:
TBD